TI 84 Plus CE: Rotating y(x) (Updated)

TI 84 Plus CE:  Rotating y(x) (Updated) 

See the original post, way back on August 13, 2012, here:  http://edspi31415.blogspot.com/2012/08/applications-and-programming-rotation.html

This is an updated version of ROTATEY1.  This version will ask you for a function (enter y(X) in quotes, very important), degree rotation, and a speed factor.  For the most detailed rotated graph, enter 1.  Higher numbers will speed up the plot but will decrease the detail of the rotated graph.

The rotated graph is plotted by two lists, L1 for the x coordinates, and L2 for the y coordinates.

TI-84 Plus CE Program ROTATEY1

"2020-02-24 EWS 84+CE"
Func
FnOff
PlotsOff
Disp "USE QUOTES"
Input "Y1=", Y1
FnOn 1
PlotsOn 1
Radian
Disp "TYPE ° FOR DEGREES","COUNTERCLOCKWISE"
Input "θ?", θ
Input "SPEED FACTOR?", F
Xmin → X
{0} → L1
{0} → L2
1 → C
For(K, Xmin, Xmax - ∆X, ∆X F)
K + ∆X F → X
augment(L1, {X cos(θ) - Y1 sin(θ)}) → L1
augment(L2, {X sin(θ) + Y1 cos(θ)}) → L2
C + 1 → C
ClrHome
Output(1,1"PROGRESS")
Output(2,1,round(100C/(319/F),2))
End
L1(2) → L1(1)
L2(2) → L2(1)
Plot1(xyLine, L1, L2, .)
ZoomStat

Download the TI-84 Plus CE version: 
https://drive.google.com/open?id=1Mop7Vfn_5EwZ2dzFrlwMzUXsTPAz7baV

Examples

Example 1: 
Y1 = "X*SIN(X)"
θ = 35°
SPEED FACTOR = 2

Example 2:
Y1 = "(X-1)^3"
θ = -60°
SPEED FACTOR = 2

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

TI 84 Plus CE: Building Piecewise Functions by Points

TI 84 Plus CE:  Building Piecewise Functions by Points

Introduction

The program PWISEBLD generates a parametric piecewise function in the form:

x(t) = t
y(t) = p(t)  (piecewise function)

The program allows the user to draw lines from 2 to 5 points.

Point 1:  (A, B)
Point 2:  (C, D)
Point 3:  (E, F)
Point 4:  (G, H)
Point 5:  (I, J)

p(t) =
(Kt + B - KA)(A ≤ t ≤ C) +
(LT + D - LC)(C < t ≤ E) +
(Mt + F - ME)(E < t ≤ G) +
(Nt + H - NG)(G < t ≤ I)

where the comparisons evaluate to either 0 (false) or 1 (true)

The program was typed on the TI-84 Plus CE but it should work with any of the TI-80 (?), TI-81 (?), TI-82, TI-83, and TI-84 families. 

TI-84 Plus Program PWISEBLD

"2020-02-24 EWS"
Param
FnOff
ClrHome
Disp "PIECEWISE BY POINTS", "PARAMETRIC MODE"
Lbl 0
Input "POINTS (2,3,4,5)?", O
iPart(O) → O
If O<2 o="" or="">5
Then
Disp "2,3,4 OR 5 ONLY"
Goto 0
End
"DATA"
"T" → X1T
Disp "(A,B)?"
Prompt A,B
A → Tmin
Disp "(C,D)?"
Prompt C,D
C → Tmax
(D - B) / (C - A) → K
"(KT + B - KA)(A ≤ T and T ≤ C)" → Str0
If O ≥ 3
Then
Disp "(E,F)?"
Prompt E,F
E → Tmax
(F - D) / (E - C) → L
Str0 + "+(LT+D-LC)(C
End
If O ≥ 4
Then
Disp "(G,H)?"
Prompt G,H
G → Tmax
(H - F) / (G - E) → M
Stro + "+(MT+F-ME)(E
End
If O = 5
Then
Disp "(I,J)?"
Prompt I,J
I → Tmax
(J - H) / (I - G) → N 
Str0 + "+(NT+H-NG)(G
End
Str0 → Y1T
"SET GRAPH" 
ZoomFit

Download the TI-84 Plus CE version: 
https://drive.google.com/open?id=1195hC6LBkR6uHCmCTjWAybSb07YwEPIa

You can use the parametric function Y1T(t) for analysis. 

Examples

Example 1: 
Three Points:  (3, 4), (5, 6), (8, 1)

Example 2:
Four Points:  (0, 0), (3, 4), (5, 6), (8, 1)

Example 3:
Five Points: (0, 0), (1, 1), (3, 6), (6, 10), (9, 12)

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Review: Victor 930-2 Scientific Calculator

Review:  Victor 930-2 Scientific Calculator

Quick Facts:

Model:  Victor 930-2
Company:  Victor
Type:  Scientific
Years:  2008 to present
Display:  10 digits
Batteries:  Solar with battery backup (LR43/LR1130)
Retail Price:  $17.99
Logic:  Algebraic, AOS
Number of Functions:  154

Product website from Victor:  https://www.victortech.com/product/930-2

Powerful One Line Calculator - The 21st Century Version of the TI-34

The Victor 930-2 calculator has the following features:

*  Trigonometric functions and their inverses
*  Rectangular/Polar Conversions
*  Degrees/Degree-Minute-Second Conversions
*  Logarithms, Power, Exponential
*  Single Variable Statistics
*  Base Conversions with Boolean Functions (AND, OR, XOR, XNOR, NOT)
*  Constant Calculations
*  Fractions

The keys have the same mapping as the original Texas Instruments (one line) TI-34 from the 1980s and 1990s.   There are some keys and functions that are labeled differently:

Victor 930-2:  [ X→M ],   TI-34:  [ STO ]
Victor 930-2:  [ M+ ], TI-34:  [ SUM ]
Victor 930-2:  [ X←→M ], TI-34:  [ EXC ]
Victor 930-2:  [ INV ],  TI-34:  [ 2nd ]
Victor 930-2:  [ DATA ], TI-34:  [ ∑+ ]
Victor 930-2:  [ DEL ], TI-34: [ ∑- ]

The Victor 930-2 has a bigger and clearer numeric display and an on-off switch. 

Constant calculations is something that might be an overlooked feature on some of these calculators, so let's take a look at how it works.  This applies to both the Victor 930-2 and the TI-34. 

Constant Calculations

For selected two argument functions, you can repeat the calculations on the second argument by entering different values and pressing the equals button [=]. 

A  (op)  B [ = ]
C [ = ]    ( C op B )
D [ = ]    ( D op B )
...

op:  +, -, ×, ÷, y^x, x√y, AND, OR

Example 1:
f(x) = x × π,  x = 4, 3, 3.8

4 [ × ] [ INV ] [ EXP ] (π) [ = ]
Result:  12.56637061

3 [ = ]   ×π is stored in memory
Result:  9.424777961

3.8 [ = ]
Result:  11.93805208

Example 2:
f(x) = x^2.5, x = π, 10.2, e

[ INV ] [ EXP ] (π) [ y^x ] 2.5 [ = ]
Result:  17.49341833

10.2 [ = ]     ^2.5 is stored in memory
Result:  332.2771137

1 [ INV ] [ LN ] (e^x) [ = ]
Result:  12.18249396

Example 3: 
B can be a multi-step in constant calculations.

f(x) = x ÷ (4^2 + 3), x = 10, 20, 50

10 [ ÷ ] [ ( ] 4 [ x^2 ] [ + ] 3 [ = ]
Result:  0.526315789

20 [ = ]    ÷(4^2 + 3) or ÷19 is stored in memory
Result:  1.052631579

50 [ = ]
Result:  2.631578947

Fractions

You can enter fractions and calculate with fractions.  However, you can only convert between fractions and decimals if you start with fractions in your calculations.  The calculator has a limit of 10 digits between the whole part, numerator, and denominator. 

Keyboard

The keyboard is OK.  I like the contrast between the black background and the font better on the Victor 930-2. 

I am irked by the protective case, as it is difficult to take the hard shell case off once the calculator is locked in place.  I prefer the slide case of the TI-34.  I may not cover the 930-2 and use a case or the box to protect the calculator. 

Verdict

If you are looking for a TI-34, consider the Victor 930-2 as it is an updated version.  It does the job.  Again, I wish the hard shell case was easier to work with. 

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Puzzle and Games: Guess The Digit

Puzzle and Games:  Guess The Digit 

Here's a game that you can play with students or to sharpen your wits.   I will let you figure out the solution and how you tackle these puzzles is up to you.

Each of the blanks, ____, needs a digit, from 0 to 9.  One of the digits fills in all the blanks in the puzzle.

Have fun!

Easy Level: One Blank

Example:  ___2 + 15 = 47

The missing digit is 3, since 32 + 15 = 47

3___ + 50 = 82 9___ + 27 = 120

___8 + 36 = 94 40 + 5___ = 97

__0 + 82 = 112 ___9 + 33 = 52

5___ + 48 = 104 42 + 3___ = 78

28 + 7___ = 103 52__ + 33 = 559

1__4 + 37 = 221 380 + __7 = 437

Medium Level: Two Blanks

Example:  8___ + ___6 = 119

Answer:  3, since 83 + 36 = 119


5__  + ___8 = 80 ___6 + ___4 = 150

8__ + ___1 = 136 7___ + 3___ = 116

5___ + ___3 = 64 ___8 + ___7 = 55

4___ + ___3 = 98 8___ + 3___ = 124

___8 + 3__ = 137 1__5 + __3 = 248

__4__ + 88 = 330 __43 + __6 = 819

7__3 + 1__6 = 969 45___ + 5__6 = 956

3__8 + __62 = 480 45___ + __45 = 798

51__ + 36___ = 878 4__8 + 38__ = 810


Harder Level: Three Blanks

4__ + 5__ + __2 = 128 5__ + __6 + 3__ = 98

3__ + __4 + __7 = 146 8__ + __5 + __3 = 172

5__ + __3 + __ 5 = 226 4__ + 5___ + 6__ = 159

__4 + __7 + ___0 = 281 __50 + 3__ + 4__ = 732

__4__ + 50___ = 846 __3___ + __6 = 147

__8__ + 5__ = 742 51__ + __6__ = 876


Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

OT: Race to the Finish Line Board Game

OT:   Race to the Finish Line Board Game 

What Is Needed

Your printer - preferably a color printer

Scissors

Markers:  the file contains four markers you can cut out (gray box), but any sort of small marker will do

A single die (use one of the dice from a pair of dice).  Alternates: playing cards of Ace through Six (Ace counts as one), six index cards labeled one through six (shuffle each time), or a calculator that can generate random integers 1-6

Rules

The object is simple:  get your marker to the finish line.  This game for at least 2 players.  You can determine the order which turns are taken. 

There are several spaces:

Green:  Lucky Space, Roll Again!  The player who lands on this space takes another turn. 

Red:  Stop!, Lose a Turn:  The player that lands here has his/her next turn skipped.

Blue:  Chance?  Draw one of the blue chance cards (see the bottom on the file).  You can add or transfer the chance cards to index cards, customize it any way you want. For young children, play without the chance cards if you want. 

I hope this game provides some entertainment in these tough times (and beyond).  Feel free to comment some creative ideas. 

You can download the jpeg and pdf files here (zip drive): 

https://drive.google.com/open?id=1LPJc5rh-2b17wtu9A6UtyaY5fkJ8Oxvl


(P.S. There is no cost)

Take care, stay sane, stay healthy, and love,


Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Using Pitch in Right Triangle Calculations

Using Pitch in Right Triangle Calculations

Using Pitch to Solve Right Triangle Lengths

In construction problems, we sometimes are working with roots and other structures that are shaped as right triangles.  In roofing applications, we are often working with the pitch of the roof.  The pitch is similar to the standard angle of right triangle.

The pitch is defined in 1 unit of rise over 12 units of run.  In the United States, the units are typically either feet or yards. 

pitch = 1 unit of rise / 12 units of run

With the right triangle, we can use similar triangles to determine that:

pitch /12 = rise / run

Knowing either one of the variables, we can use ratio calculations to determine the other.

Example 1:

Pitch: 3/12, Run:  48

Rise: 
12/48 = 3/x
x = 3 * 48 / 12
x = 12

Hypotenuse:
√(48^2 + 12^2) ≈ 49.4773

Example 2:

Pitch: 5/12, Rise: 30

Run:
5/12 = 30/x
x = 30 * 12 / 5
x = 72

Hypotenuse:
√(30^2 + 72^2) = 78

Approximating Angle with Pitch

To find the angle using pitch:

θ = atan(pitch / 12)

If you do not have a scientific calculator, you can approximate the angle by using any of the approximations (these are not the only approximation equations).   They were found using the curve fitting features of a Casio fx-9860gii.

θ ≈ 3.72674504 * p  + 2.78886014     (r^2 = 0.99084258)
θ ≈ 4.93070418 * p^0.91971679    (r^2 = 0.997149)
θ ≈ -0.1158911 * p^2 + 5.17538414 * p - 0.3498579   (r^2 = 0.9999772)

Data used:  θ to four decimal places are used. 

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Modern Casio Graphing Calculators: Function Memory

Modern Casio Graphing Calculators: Function Memory

This blog covers all the series:
*  Casio fx-7400gii (I don't believe earlier versions of the 7400 have this)
*  Casio fx-9750g, fx-9750gii
*  Casio fx-9860g, fx-9860gii, fx-9860 Slim
*  Casio Prizm fx-CG10/20
*  Casio fx-CG 50

Screenshots are from the fx-CG 50.

Note:  Casio calculators with math print (9860, CG 10, CG 20, CG 50), the menu FMEM/FUNCMEM will only appear when the calculator is set to Line Mode.   In any case, the commands will be always available throughout the Catalog and in Program editing mode. 

Menu names:  FMEM or FUNCMEM

Introduction

The calculator has 20 slots for function memory.  They can be for any variable, any amount of variables.   To access the FMEM (FUNCMEM for the fx-CG 10, fx-CG 20, and fx-CG 50) menu:  press [OPTN].  Please refer to the note above because this menu only appears in Line mode.  (although you still can access fn in the catalog).

You can store expressions to function memory one of two ways:

1.  Use a string and use the store arrow (→).

2.  From the FMEM/FUNCMEM menu, select STORE.  You will be prompted to enter a slot from 1 to 20.  Then you will be taken the list of all the functions stored in memory.  Press [EXIT].

You can clear an expression stored in fn, by storing nothing to it.  It is easiest to do this from the RUN.MAT mode.

You can paste the expression stored in fn by pressing RECALL, and entering the fn number at the prompt.  I think you can only do this in RUN.MAT mode.

Anything stored in fn can be used in evaluating expressions and mathematical commands.   See the screen shots below.  To evaluate fn, store the values in the variables first before recalling fn. 

The next screen shots show how fn can be stored in a graphing database (assuming it has the proper variables and type).

Hopefully you can find this helpful and it makes the use of Casio graphing calculators more efficient. 

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.